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1088. Confusing Number II πŸ”’

Description

A confusing number is a number that when rotated 180 degrees becomes a different number with each digit valid.

We can rotate digits of a number by 180 degrees to form new digits.

  • When 0, 1, 6, 8, and 9 are rotated 180 degrees, they become 0, 1, 9, 8, and 6 respectively.
  • When 2, 3, 4, 5, and 7 are rotated 180 degrees, they become invalid.

Note that after rotating a number, we can ignore leading zeros.

  • For example, after rotating 8000, we have 0008 which is considered as just 8.

Given an integer n, return the number of confusing numbers in the inclusive range [1, n].

 

Example 1:

Input: n = 20
Output: 6
Explanation: The confusing numbers are [6,9,10,16,18,19].
6 converts to 9.
9 converts to 6.
10 converts to 01 which is just 1.
16 converts to 91.
18 converts to 81.
19 converts to 61.

Example 2:

Input: n = 100
Output: 19
Explanation: The confusing numbers are [6,9,10,16,18,19,60,61,66,68,80,81,86,89,90,91,98,99,100].

 

Constraints:

  • 1 <= n <= 109

Solutions

Solution 1

Thinking

Count confusing numbers in \([1,n]\) for \(n\le 10^9\). Only digits \(0,1,6,8,9\) survive a rotation, so we build valid numbers digit by digit and then test the rotation.

Digit DFS from the high end enumerates mapped digits under the bound of \(n\). At a complete number we reuse the rotation check from problem \(1056\).

The table \(d\) is used both while filling and inside check; leading zeros are just the integer \(0\).

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class Solution:
    def confusingNumberII(self, n: int) -> int:
        def check(x: int) -> bool:
            y, t = 0, x
            while t:
                t, v = divmod(t, 10)
                y = y * 10 + d[v]
            return x != y

        def dfs(pos: int, limit: bool, x: int) -> int:
            if pos >= len(s):
                return int(check(x))
            up = int(s[pos]) if limit else 9
            ans = 0
            for i in range(up + 1):
                if d[i] != -1:
                    ans += dfs(pos + 1, limit and i == up, x * 10 + i)
            return ans

        d = [0, 1, -1, -1, -1, -1, 9, -1, 8, 6]
        s = str(n)
        return dfs(0, True, 0)

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class Solution {
    private final int[] d = {0, 1, -1, -1, -1, -1, 9, -1, 8, 6};
    private String s;

    public int confusingNumberII(int n) {
        s = String.valueOf(n);
        return dfs(0, 1, 0);
    }

    private int dfs(int pos, int limit, int x) {
        if (pos >= s.length()) {
            return check(x) ? 1 : 0;
        }
        int up = limit == 1 ? s.charAt(pos) - '0' : 9;
        int ans = 0;
        for (int i = 0; i <= up; ++i) {
            if (d[i] != -1) {
                ans += dfs(pos + 1, limit == 1 && i == up ? 1 : 0, x * 10 + i);
            }
        }
        return ans;
    }

    private boolean check(int x) {
        int y = 0;
        for (int t = x; t > 0; t /= 10) {
            int v = t % 10;
            y = y * 10 + d[v];
        }
        return x != y;
    }
}

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class Solution {
public:
    int confusingNumberII(int n) {
        string s = to_string(n);
        int d[10] = {0, 1, -1, -1, -1, -1, 9, -1, 8, 6};
        auto check = [&](int x) -> bool {
            int y = 0;
            for (int t = x; t; t /= 10) {
                int v = t % 10;
                y = y * 10 + d[v];
            }
            return x != y;
        };
        function<int(int, int, int)> dfs = [&](int pos, int limit, int x) -> int {
            if (pos >= s.size()) {
                return check(x);
            }
            int up = limit ? s[pos] - '0' : 9;
            int ans = 0;
            for (int i = 0; i <= up; ++i) {
                if (d[i] != -1) {
                    ans += dfs(pos + 1, limit && i == up, x * 10 + i);
                }
            }
            return ans;
        };
        return dfs(0, 1, 0);
    }
};

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func confusingNumberII(n int) int {
    d := [10]int{0, 1, -1, -1, -1, -1, 9, -1, 8, 6}
    s := strconv.Itoa(n)
    check := func(x int) bool {
        y := 0
        for t := x; t > 0; t /= 10 {
            v := t % 10
            y = y*10 + d[v]
        }
        return x != y
    }
    var dfs func(pos int, limit bool, x int) int
    dfs = func(pos int, limit bool, x int) (ans int) {
        if pos >= len(s) {
            if check(x) {
                return 1
            }
            return 0
        }
        up := 9
        if limit {
            up = int(s[pos] - '0')
        }
        for i := 0; i <= up; i++ {
            if d[i] != -1 {
                ans += dfs(pos+1, limit && i == up, x*10+i)
            }
        }
        return
    }
    return dfs(0, true, 0)
}

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function confusingNumberII(n: number): number {
    const s = n.toString();
    const d: number[] = [0, 1, -1, -1, -1, -1, 9, -1, 8, 6];
    const check = (x: number) => {
        let y = 0;
        for (let t = x; t > 0; t = Math.floor(t / 10)) {
            const v = t % 10;
            y = y * 10 + d[v];
        }
        return x !== y;
    };
    const dfs = (pos: number, limit: boolean, x: number): number => {
        if (pos >= s.length) {
            return check(x) ? 1 : 0;
        }
        const up = limit ? parseInt(s[pos]) : 9;
        let ans = 0;
        for (let i = 0; i <= up; ++i) {
            if (d[i] !== -1) {
                ans += dfs(pos + 1, limit && i === up, x * 10 + i);
            }
        }
        return ans;
    };
    return dfs(0, true, 0);
}

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